Can you please explain this with steps thank you! (The question is in the first paragraph, all the rest is just the Steps )

192 CHAPTER 6 Work and Kinetic Energy BRIDGING PROBLEM A Spring That Disobeys Hooke's Law Consider a hanging spring of negligible mass that does not obey Hooke's 3. Make a list of the unknown quantities, and decide which of law. When the spring is pulled downward by a distance x, the spring ex- these are the target variables. erts an upward force of magnitude ax, where a is a positive constant. Initially the hanging spring is relaxed (not extended). We then attach a EXECUTE block of mass m to the spring and release the block. The block stretches the spring as it falls (Fig. 6.29). (a) How fast is the block moving when 4. Calculate the work done on the block by the spring as the block it has fallen a distance x,? (b) At what rate does the spring do work on falls an arbitrary distance x. (The integral isn't a difficult one. the block at this point? (c) Find the maximum distance x2 that the spring Use Appendix B if you need a reminder.) Is the work done by stretches. (d) Will the block remain at the point found in part (c)? the spring positive, negative, or zero? 5. Calculate the work done on the block by any other forces as the SOLUTION GUIDE block falls an arbitrary distance x. Is this work positive, nega- IDENTIFY and SET UP live, or zero? 1. The spring force in this problem isn't constant, so you have to 6. Use the work-energy theorem to find the target variables. use the work-energy theorem. You'll also need Eq. (6.7) to find ( You'll also need an equation for power.) Hint: When the the work done by the spring over a given displacement. spring is at its maximum stretch, what is the speed of the block? 2. Draw a free-body diagram for the block, including your choice of co- ordinate axes. Note that x represents how far the spring is stretched, 7. To answer part (d), consider the net force that acts on the block so choose the positive x-direction to be downward, as in Fig. 6.29. On when it is at the point found in part (c). your coordinate axis, label the points x = x1 and x = x2. EVALUATE Figure 6.29 The block is attached to a spring that does not obey Hooke's law. 8. We learned in Section 2.5 that after an object dropped from rest Block is attached has fallen freely a distance x1. its speed is V2gx,. Use this to to end of relaxed decide whether your answer in part (a) makes sense. In addition, WWW spring, then released."s.;. ask yourself whether the algebraic sign of your answer in part (b) makes sense. 9. Find the value of x where the net force on the block would be zero. How does this compare to your result for x2? Is this con- sistent with your answer in part (d)? Positive x is downward. PROBLEMS .., ..: Difficulty